A parametric representation of totally mixed Nash equilibria

Autores
Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Sabia, Juan Vicente Rafael
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player´s strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure.
Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Perrucci, Daniel Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sabia, Juan Vicente Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
NONCOOPERATIVE GAME THEORY
NASH EQUILIBRIA
POLYNOMIAL EQUATION SOLVING
MULTIHOMOGENEOUS RESULTANTS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/244847
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/244847
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A parametric representation of totally mixed Nash equilibriaJeronimo, Gabriela TaliPerrucci, Daniel RobertoSabia, Juan Vicente RafaelNONCOOPERATIVE GAME THEORYNASH EQUILIBRIAPOLYNOMIAL EQUATION SOLVINGMULTIHOMOGENEOUS RESULTANTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player´s strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure.Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Perrucci, Daniel Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sabia, Juan Vicente Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaPergamon-Elsevier Science Ltd2009-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/244847Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Sabia, Juan Vicente Rafael; A parametric representation of totally mixed Nash equilibria; Pergamon-Elsevier Science Ltd; Computers & Mathematics With Applications (1987); 58; 6; 9-2009; 1126-11410898-1221CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2009.06.043info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0898122109004568?via%3Dihubinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0703436info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:58:59Zoai:ri.conicet.gov.ar:11336/244847instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:58:59.927CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A parametric representation of totally mixed Nash equilibria
title A parametric representation of totally mixed Nash equilibria
spellingShingle A parametric representation of totally mixed Nash equilibria
Jeronimo, Gabriela Tali
NONCOOPERATIVE GAME THEORY
NASH EQUILIBRIA
POLYNOMIAL EQUATION SOLVING
MULTIHOMOGENEOUS RESULTANTS
title_short A parametric representation of totally mixed Nash equilibria
title_full A parametric representation of totally mixed Nash equilibria
title_fullStr A parametric representation of totally mixed Nash equilibria
title_full_unstemmed A parametric representation of totally mixed Nash equilibria
title_sort A parametric representation of totally mixed Nash equilibria
dc.creator.none.fl_str_mv Jeronimo, Gabriela Tali
Perrucci, Daniel Roberto
Sabia, Juan Vicente Rafael
author Jeronimo, Gabriela Tali
author_facet Jeronimo, Gabriela Tali
Perrucci, Daniel Roberto
Sabia, Juan Vicente Rafael
author_role author
author2 Perrucci, Daniel Roberto
Sabia, Juan Vicente Rafael
author2_role author
author
dc.subject.none.fl_str_mv NONCOOPERATIVE GAME THEORY
NASH EQUILIBRIA
POLYNOMIAL EQUATION SOLVING
MULTIHOMOGENEOUS RESULTANTS
topic NONCOOPERATIVE GAME THEORY
NASH EQUILIBRIA
POLYNOMIAL EQUATION SOLVING
MULTIHOMOGENEOUS RESULTANTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player´s strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure.
Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Perrucci, Daniel Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sabia, Juan Vicente Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player´s strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure.
publishDate 2009
dc.date.none.fl_str_mv 2009-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/244847
Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Sabia, Juan Vicente Rafael; A parametric representation of totally mixed Nash equilibria; Pergamon-Elsevier Science Ltd; Computers & Mathematics With Applications (1987); 58; 6; 9-2009; 1126-1141
0898-1221
CONICET Digital
CONICET
url http://hdl.handle.net/11336/244847
identifier_str_mv Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Sabia, Juan Vicente Rafael; A parametric representation of totally mixed Nash equilibria; Pergamon-Elsevier Science Ltd; Computers & Mathematics With Applications (1987); 58; 6; 9-2009; 1126-1141
0898-1221
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2009.06.043
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0898122109004568?via%3Dihub
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0703436
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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